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arXiv:cond-mat/0112206 · Physical review. B, Condensed matter

Quantum phase transition in coupled spin ladders

Luca Capriotti, Federico Becca

Published Feb 6, 2002• 17 citations
arXivHTMLPDF

Abstract

The ground state of an array of coupled, spin-$\frac{1}{2},$ antiferromagnetic ladders is studied using spin-wave theory, exact diagonalization (up to 36 sites), and quantum Monte Carlo techniques (up to 256 sites). Our results clearly indicate the occurrence of a zero-temperature phase transition between a N\'eel ordered and a nonmagnetic phase at a finite value of the interladder coupling $({\ensuremath{\alpha}}_{c}\ensuremath{\simeq}0.3).$ This transition is marked by remarkable changes in the structure of the excitation spectrum.

DOI
10.1103/physrevb.65.092406

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We study the dimer XXZXXZXXZ spin model on two-leg ladders with isotropic Heisenberg interactions on the rung and anisotropic XXZXXZXXZ interactions along the rail in an external field. Combining both analytical and numerical methods, we set up the ground state phase diagram and investigate the quantum phase transitions and the properties of rich phases, including the full polarized, singlet dimer, Luttinger liquid, triplon solid, and a non-trivial antiferromagnetic phases with gap. The analytical analyses based on solvable effective Hamiltonians are presented for clear view of the phases and transitions. Quantum Monte Carlo and exact diagonalization methods are employed on finite system to verify the exact nature of the phases and transitions. Of all the phases, we pay a special attention to the gapped antiferromagnetic phase, which is disclosed to be a non-trivial one that exhibits the time-reversal symmetry. We also discuss how our findings could be detected in experiment in the light of ultracold atoms technology advances.